Question

question 9
0/1 pt 5 19 details
when equal masses of the following compounds undergoes complete combustion, which chemicals will produce the least co₂?
4-greatest
2
3
1-least
a

b
c
d
a. benzene, c₆h₆
b. glucose, c₆h₁₂o₆
c. cyclohexane, c₆h₁₂
d. methane, ch₄
subr d estion

Explanation:

Step1: Analyze Carbon Content

To determine which compound produces the least \( \text{CO}_2 \) upon combustion, we analyze the carbon - hydrogen - oxygen (for glucose) ratio. The key idea is that for a given mass of a compound, the amount of \( \text{CO}_2 \) produced is related to the mass fraction of carbon in the compound. A lower mass fraction of carbon will lead to less \( \text{CO}_2 \) production.

• For Benzene (\( \text{C}_6\text{H}_6 \)):

The molar mass of \( \text{C}_6\text{H}_6 \) is \( M_{C_6H_6}=6\times12 + 6\times1=78\space g/mol \). The mass of carbon in one mole of \( \text{C}_6\text{H}_6 \) is \( 6\times12 = 72\space g \). The mass fraction of carbon, \( f_{C, C_6H_6}=\frac{72}{78}\approx0.923 \).

• For Glucose (\( \text{C}_6\text{H}_{12}\text{O}_6 \)):

The molar mass of \( \text{C}_6\text{H}_{12}\text{O}_6 \) is \( M_{C_6H_{12}O_6}=6\times12+12\times1 + 6\times16 = 180\space g/mol \). The mass of carbon in one mole of \( \text{C}_6\text{H}_{12}\text{O}_6 \) is \( 6\times12 = 72\space g \). The mass fraction of carbon, \( f_{C, C_6H_{12}O_6}=\frac{72}{180} = 0.4 \).

• For Cyclohexane (\( \text{C}_6\text{H}_{12} \)):

The molar mass of \( \text{C}_6\text{H}_{12} \) is \( M_{C_6H_{12}}=6\times12+12\times1 = 84\space g/mol \). The mass of carbon in one mole of \( \text{C}_6\text{H}_{12} \) is \( 6\times12 = 72\space g \). The mass fraction of carbon, \( f_{C, C_6H_{12}}=\frac{72}{84}\approx0.857 \).

• For Methane (\( \text{CH}_4 \)):

The molar mass of \( \text{CH}_4 \) is \( M_{CH_4}=12 + 4\times1=16\space g/mol \). The mass of carbon in one mole of \( \text{CH}_4 \) is \( 12\space g \). The mass fraction of carbon, \( f_{C, CH_4}=\frac{12}{16} = 0.75 \).

Step2: Compare Mass Fractions

We compare the mass fractions of carbon in each compound: \( 0.4\space (glucose)<0.75\space (methane)<0.857\space (cyclohexane)<0.923\space (benzene) \). Since glucose has the lowest mass fraction of carbon among the given compounds, when equal masses of these compounds undergo complete combustion, glucose will produce the least amount of \( \text{CO}_2 \).

Answer:

b. Glucose, \( \text{C}_6\text{H}_{12}\text{O}_6 \)